Towards a Direct Measurement of the Quark Orbital Angular Momentum Distribution

TL;DR

This paper compares two definitions of quark orbital angular momentum using Fourier transforms of Wigner distributions and twist-three GPDs, revealing their relation and underlying correlations.

Contribution

It derives a relation between two different definitions of partonic orbital angular momentum, clarifying their connection and underlying physical correlations.

Findings

Established a relation between $F_{14}$ and $ ilde{E}_{2T}$ definitions.

Clarified the physical interpretation of spin and transverse momentum correlations.

Analyzed gauge link structures affecting the definitions.

Abstract

We discuss two different definitions of partonic orbital angular momentum given in the literature in terms of the Fourier transform of a Wigner distribution, $F_{14}$, and a twist three generalized parton distribution, $\tilde{E}_{2T}$, respectively. We derive a relation between the two definitions which reflects their specific spin and intrinsic transverse momentum/transverse space correlations as well as their gauge link structure.